Scholars' Mine Masters Theses Student Theses and Dissertations Spring 2013 Robust methods for construction of global potential energy surfaces Phalgun Lolur Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Chemical Engineering Commons Department: Recommended Citation Lolur, Phalgun, "Robust methods for construction of global potential energy surfaces" (2013). Masters Theses. 5372. https://scholarsmine.mst.edu/masters_theses/5372 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. ROBUST METHODS FOR CONSTRUCTION OF GLOBAL POTENTIAL ENERGY SURFACES by PHALGUN LOLUR A THESIS Presented to the Faculty of the Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE IN CHEMICAL ENGINEERING 2013 Approved by Daniel Forciniti, Advisor Richard Dawes, Co-Advisor Jee-Ching Wang iii ABSTRACT This thesis is about the development of robust methods for construction of global potential energy surfaces to study the spectroscopy and dynamics of molecular systems. A potential energy surface represents the electronic energy of a molecule as a function of its geometry. This is central to how chemists view molecular systems in terms of motion across a rich energy landscape where barriers separate wells corresponding to different stable structures. The range of molecular distortions defines the potential energy surface. Computing the potential energy surface of a molecule has become a fundamental operation in modern theoretical chemistry studies. The Born–Oppenheimer approximation simplifies the Schrödinger equation (since the nuclei move slowly relative to the electrons), and enables computation of energies forming the surface. In order to develop a highly accurate surface, it is generally required to compute energies at many (typically thousands) molecular geometries. These data are then fit together using an interpolative scheme to form an analytic function. Due to interaction between states, in order to develop a surface for a particular state of interest, one often needs to include several states. In a multistate calculation, states are optimized for some choice of relative weights. It is necessary to dynamically adjust the weights, as the geometry is varied, in order to obtain a smooth and continuous surface (as using fixed weights can lead to disruptive discontinuities where states switch character). This project developed a weighting scheme based on an energy dependent functional designed to produce high accuracy and robust convergence for global surfaces. This method has been successfully demonstrated on ozone. The theoretical calculations are in good agreement with experiments, producing a significant improvement of the rate constant for the O + O2 exchange reaction. iv ACKNOWLEDGMENTS It wouldn’t have been possible for me to write this thesis if not for all the help I’ve received along the way to make it a success. First of all, I would like to thank my advisors Dr. Richard Dawes and Dr. Daniel Forciniti for their insight and guidance throughout the process. Dr. Dawes has been extremely understanding and patient with me. Without his support, stimulation, intellectual insight and constructive criticism, this work would not have been a possibility. He has been a constant source of inspiration for me. I would also like to thank Dr. Jee-Ching Wang, who was on my committee along with my advisors, for all the advice he has given me over the past three years. I am grateful for all the faculty and staff of the Chemical Engineering and the Chemistry departments of Missouri S&T for helping me grow as a student, day by day, over the duration of my course. I would also like to thank my fellow graduate students for being there for me. I got to learn a lot of things from them about how to go on about my research, directly or indirectly, in many ways. On a personal note, I would like to dedicate this thesis to my late father, L.K. Guru Prasad and my wonderful mother, Padmaja Dabir, for her constant support, encouragement and love throughout my life for as far as I can remember. I would also like to dedicate this thesis to my sister, grandparents, aunts, uncles, cousins and my other family members for everything they have done for me and above all, for being there for me. Speaking of family, I need to thank my extended family – my friends, who have been my constant pillars of support. They have been instrumental in making me what I am today and no words can express how grateful I am to them for being there through my highs and lows. To all of them, I dedicate this work. v TABLE OF CONTENTS Page ABSTRACT .....................................................................................................................iii ACKNOWLEDGMENTS ...............................................................................................iv LIST OF ILLUSTRATIONS ...........................................................................................vi LIST OF TABLES ...........................................................................................................vii SECTION 1. INTRODUCTION ...........................................................................................1 2. BACKGROUND .............................................................................................11 3. ELECTRONIC STRUCTURE CALCULATIONS .........................................15 4. RESULTS ........................................................................................................21 5. CONCLUSIONS AND REMARKS ...............................................................32 APPENDICES A. COMMUNICATION: HIGHLY ACCURATE OZONE FORMATION POTENTIAL AND IMPLICATIONS FOR KINETICS ................................37 B. LIST OF PUBLICATIONS ...........................................................................52 REFERENCES ................................................................................................................53 VITA ................................................................................................................................58 vi LIST OF ILLUSTRATIONS Figure Page 1.1 CASSCF calculations for the six lowest A1 states for BeOBe, fixing the angle at 180°, done at the avdz level demonstrate the advantages of dynamic weighting .......8 1.2 CASSCF calculations for BeOBe, fixing the angle at 180°, done at the avdz level demonstrate the importance of including multiple states ..................................9 2.1 Physical structure of molecular oxygen and ozone ....................................................11 2.2 Ozone concentration in the atmospheric layers .........................................................12 2.3 Chapman cycle - formation and destruction of ozone from molecular oxygen .........13 4.1 Relaxed dissociation path for ozone showing submerged reef barrier and vdW well obtained in single-state MRCI calculation with relaxed-reference Davidson correction and 2s orbitals closed in 13-state DW-SA-CASSCF reference .................23 4.2 Cut through transition region showing reef barrier obtained in single-state MRCI calculation and with relaxed reference Davidson correction ...........................24 4.3 Cut through transition region showing reef barrier obtained in single-state MRCI calculations and two-state MRCI calculations ...............................................25 4.4 Cut through transition region comparing rotated reference and relaxed reference Davidson corrections for two-state MRCI calculations .............................27 4.5 Cut through transition region comparing rotated reference Davidson- corrected two-state MRCI energies ...........................................................................29 5.1 Minimal energy path for O3 formation along an O-O bond length obtained in this work and its comparison with that on the hybrid PES of Babikov et al. ...................33 vii LIST OF TABLES Table Page 4.1 Geometric parameters along a relaxed dissociation path ...........................................22 4.2 Calculated dissociation energies (cm-1) for MRCI and with applied relaxed or modified Davidson corrections ..................................................................................30 1. INTRODUCTION By the end of the nineteenth century, many scientists believed that most of the fundamental laws and equations had already been worked out. The only improvements that they expected were minor refinements in the theories to get that extra decimal place of accuracy in their calculations. But everything changed when quantum mechanics came into the picture in the early twentieth century. Max Planck, who is considered as the father of the quantum theory, came up with his hypothesis (which was based on the work of Wilhelm Wien) that energy is emitted and absorbed in distinct packets called “quanta” as early as the year 1900.1 But the scientific community didn’t embrace the idea seriously until another great physicist, Albert Einstein, made a similar assumption to explain the photoelectric effect in 1905. He worked on quantum mechanics for the next two years and proposed a model that could solve for the specific heat of solids, based on Planck’s assumption that even